The Unique Minimum State Variable RE Solution is E-Stable in All Well Formulated Linear Models

The recent appearance of major publications by Evans and Honkapohja (1999, 2001) has stimulated new interest in the relationship between the linked concepts of E-stability and least-squares learnability, featured in their work, and the minimum-state-variable solution concept promoted by McCallum (1983, 1999) and used by many researchers for rational expectations (RE) analysis. In the present paper it will be argued that the connection is much tighter, at least for linear models, than the discussion of Evans and Honkapohja (1999, 2001) seems to suggest—and than is generally believed. Indeed, it will be shown that, for all linear models (within a very wide class) that satisfy the property of being well formulated, the unique minimum-state-variable (MSV) solution is E-stable and therefore least-squares (LS) learnable.